My philosophy is that it is hard, but not impossible, to beat the market, and that it is easy, and imperative, to save on taxes and money management costs. I graduated from Harvard in 1973 with a degree in linguistics and applied math. I have been a journalist for 40 years, and was editor of Forbes magazine from 1999 to 2010. Tax law is a frequent subject in my articles. I have been an Enrolled Agent since 1979. You can email me at --williambaldwinfinance -- at -- gmail -- dot -- com.

$500 Million Jackpot: Calculating Your Odds

The Mega Millions lottery drawing Friday night will deliver a jackpot estimated at $540 million. Your odds of picking the winning combo are 175.7 million to one. Divide one number by the other. That means a ticket is worth $3.07, right? Maybe you should buy as many as you can?

Not so fast. There’s a little more to the math here. You have to allow for not only the long odds that you’ll pick the right numbers but also the short odds that you will be sharing that jackpot.

It turns out that each ticket has a value a bit shy of the one dollar you pay for it. But at least you’re doing a lot better than you would in a lottery that doesn’t have a carryover from the previous drawing. If you like to buy lottery tickets, now is a good time.

I’ll explain how you calculate odds, and how to improve them slightly. I’ll also give you some sad news about the time value of money and the taxation of gamblers.

The jackpot is a giant one because no one picked the numbers to win the $363 million pot offered in Tuesday’s drawing. That sum is added to a percentage of the take from ticket sales over the next 72 hours to arrive at the Mar. 30 pot.

The frenzy of ticket buying that began Wednesday leads to an official projection of a $540 million pot. I would bet that the operators are lowballing here. My speculative guess: a pot near $600 million, with just under 620 million tickets sold. That would be more than triple the number sold for the Tuesday draw. You can buy tickets in 42 states plus the District of Columbia.

Biggest jackpot so far: $390 million in March 2007, shared by two winning tickets.

To win the big one you have to pick which five numbers between 1 and 56 will be pulled, and then pick a second number between 1 and 46. The order of the first five is not important and there are no repeats.

Here’s how you get the odds: multiply 56x55x54x53x52, then divide by 5x4x3x2 to get 3.82 million. Now multiply that by 46 to get 175.7 million.

If you get the five-number combo but not the 1-to-46 play, then you win a flat $250,000 (except in California, where it gets more complicated). Lesser matches have smaller payoffs, ranging down to $2.

Post Your Comment

Post Your Reply

Forbes writers have the ability to call out member comments they find particularly interesting. Called-out comments are highlighted across the Forbes network. You'll be notified if your comment is called out.

This story contains perhaps the biggest blow imaginable to classic economic’s assumption that people are perfectly rational, maximizing economic actors: Three people won the lottery *and then didn’t cash in their tickets.* Wow.

While I agree with the notion that people aren’t “perfectly rational”, those winners could have easily misplaced their tickets or had them destroyed before the drawing. Plenty of times I’ve kept a $1 winner in my wallet past the expiration date.

You could probably prove that it is not economically rational, aftertax, to start a new company, but people do that anyway and I’m glad they do. What are the odds you’ll have something as big as Facebook? Not much better than the odds in the lottery.

Two economists are walking down the street; one looks down for a moment, turns to the other and says, “I think there’s a $100 bill lying on the ground there”. The other economist shakes his head and continues walking, “Can’t be – if there were, someone would’ve picked it up already.”

To get that number, you assume that the number of tickets sold is 616 million. However, since the prize money has rolled over many times, most of those tickets are no longer good. Wouldn’t the the tickets sold since the last drawing be the only ones be eligible for the new jackpot?

Or are you saying that 616 million tickets will be sold from Tues to Friday?